Algebra Examples

${(x^{7} {(- y^{8} z^{5})}^{2})}^{3}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $- y^{8} z^{5}$ .

${(x^{7} ({(- y^{8})}^{2} {(z^{5})}^{2}))}^{3}$

Step 1.2

Apply the product rule to $- y^{8}$ .

${(x^{7} ({(- 1)}^{2} {(y^{8})}^{2} {(z^{5})}^{2}))}^{3}$

Step 2

Rewrite using the commutative property of multiplication.

${({(- 1)}^{2} x^{7} {(y^{8})}^{2} {(z^{5})}^{2})}^{3}$

Step 3

Raise $- 1$ to the power of $2$ .

${(1 x^{7} {(y^{8})}^{2} {(z^{5})}^{2})}^{3}$

Step 4

Multiply $x^{7}$ by $1$ .

${(x^{7} {(y^{8})}^{2} {(z^{5})}^{2})}^{3}$

Step 5

Multiply the exponents in ${(y^{8})}^{2}$ .

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Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x^{7} y^{8 \cdot 2} {(z^{5})}^{2})}^{3}$

Step 5.2

Multiply $8$ by $2$ .

${(x^{7} y^{16} {(z^{5})}^{2})}^{3}$

Step 6

Multiply the exponents in ${(z^{5})}^{2}$ .

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Step 6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x^{7} y^{16} z^{5 \cdot 2})}^{3}$

Step 6.2

Multiply $5$ by $2$ .

${(x^{7} y^{16} z^{10})}^{3}$

Step 7

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 7.1

Apply the product rule to $x^{7} y^{16} z^{10}$ .

${(x^{7} y^{16})}^{3} {(z^{10})}^{3}$

Step 7.2

Apply the product rule to $x^{7} y^{16}$ .

${(x^{7})}^{3} {(y^{16})}^{3} {(z^{10})}^{3}$

Step 8

Multiply the exponents in ${(x^{7})}^{3}$ .

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Step 8.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{7 \cdot 3} {(y^{16})}^{3} {(z^{10})}^{3}$

Step 8.2

Multiply $7$ by $3$ .

$x^{21} {(y^{16})}^{3} {(z^{10})}^{3}$

Step 9

Multiply the exponents in ${(y^{16})}^{3}$ .

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Step 9.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{21} y^{16 \cdot 3} {(z^{10})}^{3}$

Step 9.2

Multiply $16$ by $3$ .

$x^{21} y^{48} {(z^{10})}^{3}$

Step 10

Multiply the exponents in ${(z^{10})}^{3}$ .

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Step 10.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{21} y^{48} z^{10 \cdot 3}$

Step 10.2

Multiply $10$ by $3$ .

$x^{21} y^{48} z^{30}$